8010 Practice Exam Questions with Answers Operational Risk Manager (ORM) Exam Certification

Economic capital is a measure of the level of capital needed to maintain adesired credit rating. Regulatory capital is the amount of capital required to be held by regulation, and this may be quite different from economic capital. Book value is an accounting measure reflecting the assets minus liabilities as measured per accounting rules, this is often expressed per share. Shareholders' equity is a narrow term which is the amount of capital attributable to the shareholders and includes paid up capital and reserves but not long term debt or other non-equity funding.

Therefore Choice 'b' is the correct answer.

Collateral, limits to avoid credit exposure concentrations, termination rights based upon credit ratings, third party guarantees and credit derivatives are all tools or instruments that financial institutions use to manage their credit risk. A cumulative accuracy plot measures the accuracy of ratings, and is not a tool for managing credit risk. Therefore Choice 'b' represents the correct answer.

The distance to default is the number of standard deviations that expected asset values are away from the default point. The expression in Choice 'd' represents distance to default. Choice 'd' is the correct answer. The other choices are incorrect.

Other than Choice 'c', all others represent valid approaches to allocate economic capital to underlying business units. There is no such thing as 'fixed ratioeconomic capital contribution'

Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analyticaldistribution, such as log-normal or other that approximates the distribution best represented by known data - whether from the internal loss database, the external loss database or scenario data. A 'risk functional' is a measure of the deviation of the model distribution from the risk's actual severity distribution. It assigns a penalty value for the deviation, using a statistical measure, such as the KS distance (Kolmogorov-Smirnov distance).

The problem of finding the right distribution then becomes the problem of optimizing the risk functional. For example, if F is the model distribution, and G is the actual, or empirical severity distribution, and we are using the KS test, then the Risk Functional R is defined as follows:

Note that supx stands for 'supremum', which is a more technical way of saying 'maximum'. In other words, we are calculating the maximum absolute KS distance between the two distributions. (Note that the KS distance is the max of the distance between identical percentiles of the two distributions using the CDFs of the two.)

Once the risk functional is identified, we can minimize it to determine the best fitting distribution for severity.

Statement I is correct. Retail Risk Based Pricing (RRBP) involves the use of borrower specific data (such as FICO scores, average balances etc) to arrive at credit decisions. These 'retail' credit decisions may include decisions on whether to grant a line of credit, a mortgage, issue a credit card, or any of the various other retail activities abank may be dealing with. At the same time, this data can also be used to price the product, in addition to providing a yes or no credit decision so that risky borrowers are charged more than less risky borrowers.

Statement II is not correct, because an integrated Risk Information Management Environment includes three elements - people, processes and technology (and not just people and processes).

Statement III is correct. An LDM is a blue print of an organization's data, and describes the relationships between the various data elements.

Statement IV is not correct because reference data and metadata are not the same thing. Reference data refers to relatively static data, such as customer name (while actual transactions may not be so static). Metadata refers to data about data, and is stored in a data dictionary.

Therefore Choice 'b' is the correct answer and the rest are incorrect.

A situation where a firm has more liabilities than assets does not necessarily implydefault, so long as the firm is able to pay its obligations when they come due. Therefore, short term debts have a greater bearing on a firm's default than longer term debt. However, this is not to say that merely having enough to pay off the short term debts (ie debts due within one year) is enough to avoid default. Over time, the long term debt will also be turning to short term debt, and it may not be possible for the firm to roll over its liabilities without lenders considering the long term debt. The KMV approach considers the entire short term debt and half of the long term debt as the critical value of assets below which default will be triggered. Therefore Choice 'c' is the correct answer.

An error rate of 10 basis points means the number of errors expected in a day will be 15 (recall that 100 basis points = 1%). Therefore the total number of errors expected in a year will be 15 x250 = 3750. Choice 'a' is the correct answer.

All the reasons and risks presented above are valid reasons for using scenario analysis, except V and VI - ie, the need to reduce the complexity of calculations is not a valid reason for using scenario analysis. Similarly, making operational risk capital estimates match management's desired capital allocation targets is also not a valid reason. Capital calculations are intended to provide adequate capital for managing the risk from operations, regardless of what management may desire them to be.

Economic capital in respect of credit risk is intended to absorb unexpected losses. Unexpected losses are the losses above and beyond expected losses and up to the level ofconfidence that economic capital is being calculated for. The capital required to cover unexpected losses in this case is E - U, and therefore Choice 'a' is the correct answer.

This question does raise an important point - are expected losses a part of economic capital, or are they not? Different text books say different things, and sometimes they say both the things. I have tried to take an approach that uses what I read in the PRMIA handbook.

This writeup - http://www.riskprep.com/all-tutorials/37-exam-3/111-credit-var-an-intuitive-understanding - may help clarify things further.

A bullet bond is a bond that pays coupons covering interest during the life of the bond and theprincipal at maturity. An amortizing loan pays the interest as well as a part of the principal with every payment. Therefore, the exposure of the amortizing loan continually reduces, and approaches zero towards the end of its life. The bullet bond will always have a higher exposure at any time during its life when compared to an equivalent amortizing loan. Hence Choice 'd' is the correct answer.

A high score under the probit and logit models indicates a higher default risk, while under Altman's methodology it indicates a lower default risk. Therefore Choice 'd' is the correct answer.

QUESTIONNO: 138

For a corporate issuer, which of the following can be used to calculate market implied default probabilities?

I. CDS spreads

II. Bond prices

III. Credit rating issued by S&P

IV. Altman's scoring model

A. III and IV

B. I and II

C. I, II and III

D. II and III

Answer: B

Generally, the probability of default is an input into determining the price of a security. However, if we know the market price of a security, we can back out the probability of default that the market is factoring into pricing that security. Market implied default probabilities are the probabilities of default priced into security prices, and can be determined from both bond prices and CDS spreads. Credit ratings issued by a credit agency do not give us 'market implied default probabilities', and neither does an internal scoring model like Altman's as these do not consider actual market prices in any way.

Therefore Choice 'b' is the correct answer and the others are not.

Top down approaches rely upon available data such as total capital, income volatility, peer group information etc and attempt to imply the capital attributable to operational risk. They do not consider firm specific scenarios or causal factors. Bottom up approaches on the other hand attempt to determine operational risk capital based upon an identification and quantification of firm specific risks. Bottom up approaches help determine a traditional loss distribution from which capital requirements can be determined at a given level of confidence.

Therefore Choice 'd' is the correct answer.

Theprobability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be

= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))

=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.

The cash flows from the treasury bond would be 1.04. These two should be equal, ie,

1.04 = (1- p)*1.085, implying p = 4.15%.

(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)

The commercial paper has greater credit risk as the entire notional is outstanding. On the forward contract, only the replacement value of the contract, which normally would be a mere fraction of the notional, would be at risk.

Therefore Choice 'd' is the correct answer.

This question relates to fitting a distribution to the true severity of the operational risk loss we are trying to model. The quality of the fit, or the precision of the fit, has two elements to the difference between the severity as represented by our model and the true severity. To understand this, consider the three data points below:

a. The true severity,

b. The best approximation of the true severity in the model space, and

c. The fit based on the dataset.

- True severity is what we are trying to model.

- The model space refers to the collection of analytical distributions (log-normal, burr etc) that we are considering to arrive at the estimate of the severity.

- The 'best approximation of the true severity in the model space' is reached byestimating the parameters of the distribution that optimizes the risk functional.

- The 'fit' is the actual parameter estimates we settle for with the distribution we have determined best fits the true estimate of our severity. When estimating parameters,we have various methods available for estimation - the least squares method, the maximum likelihood method, for example, and we can get different estimates depending upon the method we choose to use.

Our severity model will be different from the true severity, and the total difference can be split into two types of errors:

1. Fitting error, represented by 'c - b' above: The difference between the fit based on the dataset and the best approximation of the true severity is called 'fitting error', ie, a measure of the extent to which we could have estimated the parameters better.

2. Approximation error, represented by 'b - a' above: Approximation error is the difference between the true severity, and the best approximation of the true severity that can be achieved within the model space is called 'approximation error'.

One can reduce the approximation error by expanding the model space by adding more distributions. This will reduce the approximation error, but generally has the effect of increasing the fittingerror because the complexity of the model space increases, and there are more ways to fit to the true severity.

Choice 'a' is the correct answer. The other choices represent non-sensical statements.

In a bankruptcy, equity ranks last. Preferred equity is one level above equity. Senior debt gets paid outfirst compared to junior debt, and secured debt is paid out first to the extent of the asset securing it (after which it counts as unsecured debt). Accounts payable and other short term liabilities are treated like unsecured creditors. Debtor-in-possession(DIP) financing ranks higher than any other asset as it is financing secured after the bankruptcy to continue the business.

Based on the above, statement I does not represent a correct ordering of seniority as equity is paid last. Similarly, DIP financingreceives higher priority than even secured debt, and therefore statement IV is incorrect. Therefore the only correct statements are II and III and Choice 'a' is the correct answer.

Loss provisioning is intended to cover expected losses. Economic capital is expected to cover unexpected losses. No capital or provisions are set aside for losses in excess of unexpected losses, which will ultimately be borne by equity.

Choice 'd' is the correct answer.

Assuming timeinvariance and the Markov property, it is easy to calculate the transition matrix for any time period as P^n, where P is the given transition matrix for one period and n the number of time periods that we need to compute the new transition matrix for. ThusChoice 'b' is the correct answer.

According to the option pricing approach developed by Merton, the shareholders of a firm have a put on the assets of the firm where the strike price is equal to the face value of the firm's debt. This is just a more complicated way of saying that the debt holders are entitled to all the assets of the firm if these assets are insufficient to pay off the debts, and because of limited liability of the shareholders of a corporation this part payment will fully extinguish thedebt.

A firm will default on its debt if the value of the assets falls below the face value of the debt. Therefore Choice 'a' is the correct answer. All other choices are incorrect.

(There are two ways to consider this sort of optionality, and I have mentioned only one for this question:

1. The equity holders can sell the assets of the firm to the debt holders at a price equal to the face value of the debt, ie a put. (ie they can extinguish their liability to the debt holders in full by handing them the assets of the firm, effectively selling them the assets at the value of the debt)

2. The equity holders have a long position in a call option where they can keep the assets of the firm by paying a price equal to the face value of the debt (ie, they can pay off the debt holders and keep the assets)

For this question, perspective 1 applies but you should be aware of the second one too as a question may reference that view point.)

Offsetting trades with other counterparties will not reduce credit exposure to a given counterparty. All other choices represent means of reducing credit risk. Therefore Choice 'c' is the correct answer.

Choice 'c' is the correct answer. Refer to the detailed loss event type classification under Basel II (see Annex 9 of the accord). Youshould know the exact names of all loss event types, and examples of each.

Since the business units are uncorrelated, we can get the combined EC as equal to the square root of the sum of the squares of the individual EC estimates.Therefore Choice 'a' is the correct answer. [=SQRT(100^2+200^2+150^2)]

All the listed variables are relevant to management monitoring the credit risk profile of an institution, therefore Choice 'd' is the correct answer.

KMV Moody's uses a proprietary database to convert the distance to default to expected default probabilities.

The credit risk horizon for credit VaR is generally one year.Therefore Choice 'b' is the correct answer.

Bank B's exposure is measured by the price it paid for the bonds, which in this case is $7m ($10m x 70/100). Hence Choice 'c' represents the correct answer.

(Note that the question is asking for 'exposure' and not the legal claim in the event of default. The legal claim in the event of default would be the full notional of $10m. )

The initial issue price and issue size are irrelevant.

Altman's Z-score, the Probit and the Logit models can all be used to assess the credit rating of an individual borrower. There is no such model as the 'distance todefault model', and therefore Choice 'a' is the correct answer.

Under the contingent claims approach, a firm will default on its debt when the value of its assets fall to less than the face value of the debt. Debt holders can protect themselves against such an event by buying a put on the assets of the firm, where the strike price is equal to the value of the debt. In other words, Risky Debt + Put on the firm's assets = Risk free debt. This is because if the value of the assets is greater thanthe value of the debt, they will be paid in full. If the value of the assets is lower than the value of the debt, they will exercise the put and be paid in full.

Therefore the value of the put on the firm's assets with a strike equal to the value ofthe debt represents the cost of eliminating credit risk. Choice 'b' is the correct answer.

Note that it is improbable that a put on the firm's assets is available in real life to debt holders. However, the same effect can be synthetically achieved by usingthe shares of the firm as a proxy for its assets, and shorting an appropriate number of shares. Such a synthetic put will require frequent readjustments.

CreditRisk+ treats default as a binary event, ignoring downgrade risk, capital structures of individual firms in the portfolio or the causes of default. It uses a single parameter, ? or the mean default rate, and derives credit risk based upon the Poisson distribution. Therefore Choice 'c' is the correct answer.

All of the distributions referred to in the question can be used to model the loss severity distribution for op risk.Therefore Choice 'c' is the correct answer.

Three parameters define economic credit capital: the risk horizon, ie the time horizon over which the risk is being assessed; the confidence level, ie the quintile of the loss distribution; and the definition of credit losses, ie whether mark-to-market losses are considered in addition to default-only losses. The probability of default is not a parameter within the control of the risk manager, but an input into the capital calculation process that he has to estimate. Therefore Choice 'c' is the correct answer.

The probability that the security would not default in the next 4 years is equal to the probability of survival raised to the power four. In other words, =(1 -3%)^4 = 88.53%. Choice 'b' is the correct answer.

Volatility clustering leads to levels of current volatility that can be significantly different from long run averages.When volatility is running high, institutions need to shed risk, and when it is running low, they can afford to increase returns by taking on more risk for a given amount of capital. An institution's response to changes in volatility can be either to adjust risk, or capital, or both. Accounting for volatility clustering helps institutions manage their risk and capital and therefore statements I and II are correct.

Regulatory requirements do not require volatility clustering to be taken into account (at least not yet). Therefore statement III is not correct, and neither is IV which is completely unrelated to volatility clustering.

Choice 'b' is the correct answer. All other answers are incorrect.

Refer to the detailed loss event type classification underBasel II (see Annex 9 of the accord). You should know the exact names of all loss event types, and examples of each.

All four data sources are expected to be utilized as inputs as appropriate for operational risk calculations under the advanced measurement approach. Of these, the last one, BEICF, is slightly different from the rest as it does not yield data points that becomethe basis of curve fitting or other statistical computions underlying capital calculations. It includes items such as KRIs, risk assessments etc and allow the risk manager to assess the qualitative aspects of loss data.

The probability that only none of the three bonds will default is equal to the probability of all surviving. Since default correlation is zero, we can simply multiply the probabilities of survival. Therefore the correct answer is 94% = (1 - 1%) * (1 - 2%) * (1 - 3%)

A computation of Altman's Z-score considers the following ratios:

- Working capital to total assets

- Retained earnings to total assets

- EBIT to total assets

- Market cap to debt

- Sales to total assets

Nearly all thenumbers above are accounting measures derived straight from the balance sheet or the income statement. Market capitalization is a market driven number. Therefore Choice 'c' is the correct answer as the Altman credit risk score considers both accounting andmarket based measures.

Altman's score, though computationally straightforward and intuitively easy to understand, was introduced in the late sixties and has been very accurate in predicting corporate bankruptcies, which is why it continues to be used extensively.

For a dataset with 250 observations, the top 2% of the losses will be the top 5 observations. Expected shortfall is the average of the losses beyond the VaR threshold. Therefore the correct answer is (20 + 19 + 19 + 17 + 16)/5 = 18.2m .

Note that Expected Shortfall is also called conditional VaR (cVaR), Expected Tail Lossand Tail average.

The correct answer is choice 'b'

Both statements are accurate. Basel IIrequires pooled probabilities of default to be applied to risk buckets that contain similar exposures. Also, stress testing is mandatory for both market and credit risk.

This question requires the calculation of the credit VaR of the bonds - note that in the real exam the question may not refer to 'credit' VaR, but that canbe inferred from the context, ie because the probability of default is provided, it can only be asking for the credit VaR. (Note the difference from the market risk VaR which is driven by interest rate changes affecting the value of the bonds - there are other questions addressing that calculation).

Credit VaR = Expected Value - Worst case portfolio value at the selected percentile (ie the confidence level)

Thus if we know the distribution of the portfolio value in the future, we can find out the value at the required percentile (in this case 99%), and the VaR will be the difference between this value and the expected value of the portfolio.

An important piece of information provided is that the defaults are independent, ie they are not correlated. This means joint probabilities of default or survival can be easily found by multiplying the relevant probabilities. The following outcomes are possible:

1. Both bonds default: Probability = 1% * 1% = 0.01%. Portfolio value = $0 (because both bonds have defaulted& there is zero recovery)

2. One bond defaults and the other survives: Probability = 2 * 1% * 99% = 1.98%. Portfolio value = $1m (because one bond survives with a value of $1m and the defaulted bond has a value of $0). (Note that because there are two waysin which this can happen, ie bond 1 defaults, bond 2 survives; and bond 1 survives, bond 2 defaults, we need to multiply the probability by 2).

3. Both bonds survive: Probability = 99% * 99% = 98.01%. Portfolio value = $2m.

Expected value is therefore $1.98m (which is equal to 2 * $1m * (1 - 1%), or alternatively can also be obtained by multiplying the probabilities in the above three outcomes with the value associated with each).

The future distribution of the value of the portfolio can be constructed from the three outcomes outlined above:

a. Upto the 98.01th percentile the value of the portfolio is $2m, and the VaR is zero (being greater than the expected value, so there is nothing to lose)

b. From the 98.01th percentile to the 99.99th percentile (98.01+the next 1.98%), the value of the portfolio is $1m. VaR in this range is $0.98m (=$1.98m - $1m)

c. From the 99.99th to the 100th percentile the value of the portfolio is $0, and the VaR is $1.98m.

Since the question is asking for VaR at the 99% confidencelevel, it lies in the range in 'b' above, and therefore the VaR is $0.98m.

Therefore Choice 'c' is the correct answer and the rest are incorrect.

The first two formulae describe component VaR. The last formula is the formula for Marginal VaR. Therefore I and II is the correct answer.

Component VaR is a VaR decomposition technique that allows the total VaR for a portfolio to be broken down and attributed to the components of a portfolio. The total of the component VaR for each constituent of a portfolio is equal to the VaR for the portfolio. This property is extremely useful as opposed to the standalone VaR for each constituent taken alone as it can be used for allocating trading budgets.

The Options Theoretic approach to calculating economic capital is a top-down approach that considers the value of capital as being equivalent to a calloption with a strike price equal to the notional value of the debt - ie, the shareholders have a call option on the assets of the firm which they can acquire by paying the debt holders a value equal to their notional claim (ie the face value of the debt).Therefore Choice 'a' is the correct answer and the other choices are incorrect.

The exposure at default is the greatest for the certificate of deposit as the entire notional amount is exposed to the risk of default. The other choices represent derivatives for which the current replacement value, which would be far less than notional, would be the credit exposure.

Said another way - if the counterparty were to default, the entire money in the CD would be at risk, whereas for the derivative contracts it would only be the replacement value that would be at risk.

The correct answer is choice 'a'

The correct order of steps to addressing data quality problems in an organization would include:

1. Assesing the current state

2. Designing the future state, and

3. Planning and implementation which would include identifying the gaps between the current and the desired future state, and implementation to address the gaps.

Therefore Choice 'a' is the correct answer.

Choice 'c' is incorrect because a gap analysis cannot be performed without understanding the 'as-is' (which results from understanding the current state).

Choice 'b' is non-sensical, and Choice 'd' is a flippant option (though often used in real life situations by management as an easy (and ineffective) way to escape accountability for difficult problems)

Statement I is true as expected losses are the 'cost ofdoing business' and charged against the P&L of the unit holding the exposure. When evaluating the business unit, expected losses are taken into account. Unexpected losses however require risk capital reserves to be maintained against them.

Statement II isnot true. Credit portfolio loss distributions are not symmetrical, in fact they are highly skewed and have heavy tails.

Statement III is true. The notional, or the face value of a defaulted debt is the basis for a claim in bankruptcy court, and not the market value.

Statement IV is false. In the case of over the counter instruments, the replacement value of the contract represents the amount of the claim, and not the notional amount (which can be very high!).

Statement I is correct. Economic capital is the capital available to absorbunexpected losses, and credit ratings are also based upon a certain probability of default. Economic capital is often calculated at a level equal to the confidence required for the desired credit rating. For example, if the probability of default for a AArating is 0.02%, then economic capital maintained at a 99.98% would allow for such a rating. Economic capital set at a 99.8% level can be thought of as the level of losses that would not be exceeded with a 99.8% probability.

Loss distributions are the product of the severity and frequency distributions, each of which are estimated separately. The total loss distribution is affected far more by the severity distribution than by the frequency distribution, therefore statement II is correct.

The Loss Distribution Approach (LDA) is one of the ways in which the requirements of the AMA can be satisfied, and not the other way round. Therefore statement III is incorrect.

Statement IV is correct as the total loss distribution is estimated using separate estimatesof loss frequency and distributions.

While conceptually VaR is a fairly straightforward concept, a number of decisions need to be made to select between the different choices available for the exact mechanism to be used for the calculations.

The Basel framework requires banks toestimate VaR at the 99% confidence level over a 10 day horizon. Yet this is a decision that needs to be explicitly made and documented. Therefore 'I' is a correct choice.

At various stages of the calculations, portfolio values need to be determined. The valuation can be done using a 'full valuation', where each position is explicitly valued; or the portfolio(s) can be reduced to a handful of risk factors, and risk sensitivities such as delta, gamma, convexity etc be used to value the portfolio. The decisionbetween the two approaches is generally based on computational efficiency, complexity of the portfolio, and the degree of exactness desired. 'II' therefore is one of the decisions that needs to be made.

The decision as to disclosing the VaR in financial filings comes after the VaR has been calculated, and is unrelated to the VaR calculation system a bank needs to set up. 'III' is therefore not a correct answer.

Though the Basel framework requires a 10-day VaR to be calculated, it also allows the calculation of the 1-day VaR and and scaling it to 10 days using the square root of time rule. The bank needs to decide whether it wishes to scale the VaR based on a 1-day VaR number, or compute VaR for a 10 day period to begin with. 'IV' therefore is a decision tobe made for setting up the VaR system.

Choice 'b', Choice 'c' and Choice 'a' correctly describe a bilateral close out netting as recommended by the ISDA. However Choice 'd' is not correct as it suggests individual settlement of transactions without netting which is the whole pointof bilateral close out netting.

The probability that the security would not default in the next 4 years is equal to the probability of survival at the end of the four years. In other words, =(1 - 3%)*(1 - 4%)*(1 - 4%)*(1 - 5%) = 84.93%. Choice 'd' is the correct answer.

Some risk experts have suggested the use of extreme value theory to model tail risk or extreme events for operational risk. The generalized Pareto model or the Peaks-over-Threshold (POT) model are often used to model extreme value distributions, and therefore Choice 'a' is the correct answer.

The CCAR is a supervisory mechanism adopted by the US Federal Reserve Bank to assess capital adequacy for bank holding companies it supervises. Itwas not a concept introduced by the international Basel framework.

The other three were indeed rules introduced by Basel 2.5, which was ultimately subsumed into Basel III.

Stressed VaR is just the standard 99%/10 day VaR, calculated with theassumption that relevant market factors are under stress.

The Incremental Risk Charge (IRC) is an estimate of default and migration risk of unsecuritized credit products in the

trading book. (Though this may sound like a credit risk term, it relates to market risk - for example, a bond rated A being downgraded to BBB. In the old days, the banking book where loans to customers are held was the primary source of credit risk, but with OTC trading and complex products the trading book also now holds a good dealof credit risk. Both IRC and CRM account for these.)

While IRC considers only non-securitized products, the CRM (Comprehensive Risk Model) considers securitized products such as tranches, CDOs, and correlation based instruments.

The IRC, SVaR and CRMcomplement standard VaR by covering risks that are not included in a standard VaR model. Their results are therefore added to the VaR for capital adequacy determination.

Operational risk capital estimated using the implied capital model is merely the capital that is not attributable to market or credit risk. Therefore Choice 'b' is the correct answer. All other responses are incorrect.

Expected value = $90 ($100 - 10%)

Value at 99% confidence level = $65

Therefore economic capital required at this level of confidence = $90 - $65 = $25.

Choice 'a' is the correct answer, the other choices are not.

(We can also look at it this way as explained in section III.B.6.2.2 of the handbook: Economic capital is designed to absorb unexpected losses, which areequal to total losses at a given confidence level minus expected losses. (Expected losses are to be covered by credit reserves). Total losses are $100-$65=$35, and expected losses are 10%*$100=$10, therefore economic capital should be $35-$10=$25.)

The question is asking for the probability of default over a 6 month period when the probability of annual default is known. If we let the 6 month probability of defaut be 'd', then the probability of survival at the end of 1 year would be (1 - d)^2. This we know is equal to 1 - 3% = 0.97. Therefore we can calculate 'd' to be equal to 1.51%. Choice 'c' is the correct answer, the others are incorrect.

Note that an exam question may ask for probability of the security having survived after 6 months, in which case the answer might be 1 - 1.51%. Also note that such questions will always require you to use the probability of survival (1 - probability of default) for doing the calculations. That isbecause the probabilities of survival can be multiplied over periods of time, but not probabilities of default as the first default in any period is the 'game-over' event after which neither survival nor defaults mean anything. Therefore you generally always have to get the probability of survival till a point in time, and use that for any other calculations.

Pre-settlement risk is the risk that one of the counterparties defaults prior to the date for the maturity of the transaction in question. This may be an unrelated default, in fact there may have been no default on that particular contract, but the party may have defaulted on its other obligations, or filed for bankruptcy. To deal with such cases and to protect the interests of both the parties, it is common toprovide for immediate termination of positions and settlement based on the current replacement value of the contracts. Therefore statements I and II are correct.

Statement III is correct as well - the exposure from an OTC derivative contract derives fromits current replacement value, and not the notional. If the current replacement value is negative, then the credit exposure is considered equal to zero.

Statement IV is correct as it is quite common to restate all exposures - those from credit lines, OTC derivatives etc - in loan equivalent terms prior to estimating credit risk.

The 'middle office' is a term used for the risk management function, thereforeChoice 'd' is the correct answers. The other functions describe what the 'back office' does (IT, accounting). The 'front office' includes the traders.

When a derivative position is entered into, its mark-to-market value is generally close to zero (though the notional may be high). With the passage of time, the derivative's value fluctuates in an unpredictable way, creating a counterparty exposure that may be difficult to estimate and risk manage. Counterparty risk in such cases is estimated based on Potential Future Exposure, which may be calculated using either:

a) Take the mark-to-market at present, and add a certain percentage of the notional, or

b) Perform a Monte Carlo simulation, capturing the stochastic nature of the PFE.

Therefore I and II are valid choices. MLE and parametric estimation are not methods for calculating PFE.

Internal loss data isgenerally the highest quality as it is relevant, and is 'real' as it has occurred to the organization. External loss data suffers from a significant limitation that the risk profiles of the banks to which the data relates is generally not known due to anonymization, and may likely may not be applicable to the bank performing the calculations. Therefore, replacing external loss data with external loss data is not a good idea. Statement IV is therefore incorrect.

All other approach described are valid approaches for the risk analyst to consider and implement. Therefore statements I, II and III are correct and IV is not.

The total variance of the system is 100^2 + 40^2 + 30^2 = 12500 (as variance = volatility squared). The first factor alone has a variance of 10,000, or 80%. Therefore only the first factor will be included in the final analysis, and the rest will be ignored.

Interestingly, this example highlights one of the limitations of PCA. Obviously, the second and third factors are material when considering volatility, though the effect of squaring them to get the variance makes them appear less important than they are.

increasing the timing differences between the two legs of the transaction will increase settlement risk and not reduce it. Using escrow arrangements, such as central clearing houses to settle transactions (eg the DTCC in the United States) reduces settlement risk. Cash settlements based on netting arrangements reduce settlement risk, while physical delivery combined with gross cash payments increase it.

Therefore Choice 'a' is the correct answer.

Governance structures specify the policies, principles and procedures for making decisions about corporate direction. They distribute rights and responsibiliies among stakeholders that typically include executive management, employees, the board etc. Statement I is therefore correct.

"Cybernetics is a transdisciplinary approach for exploring regulatory systems, their structures, constraints, and possibilities. In the 21st century, the term is often used in a rather loose way to imply "controlof any system using technology" (Wikipedia). Governance literature has been affected by cybernetics, which is not the same thing as information security or cyber security. Statement II is incorrect.

Corporate governance includes risk governance, and not the other way round. Therefore statement III is incorrect.

The Cadbury Report, titled Financial Aspects of Corporate Governance, was a report issued in the UK in December 1992 by "The Committee on the Financial Aspects of Corporate Governance". The report is eponymous with the chair of the committee, and set out recommendations on the arrangement of company boards and accounting systems to mitigate corporate governance risks and failures. Statement IV is therefore correct.

p = k/N. If there are N observations of which K are upto T, then p = k/N allows us to have a continuous unbroken curve which gets increasingly weighted towards the distribution selected for the tail as we move towards the 'right', ie the higher values of losses.

The other choices are incorrect and mostly nonsensical.

A PRNG (pseudorandom number generators of the kind included in statistical packages and Excel) is used to generate random numbers that are not correlated with each other, ie they are random. A Markov process is a stochastic model that depends only upon its current state. Simulation underlies many financial calculations. None of these directly relate to generating correlated multivariate normal random numbers. That job is done utilizing a Cholesky decomposition of the correlation matrix.

Specifically, a Cholesky decomposition involves the factorization of the correlation matrix into a lower triangular matrix (a square matrix all of whose entries above the diagonal are zero) and its transpose. This can then be combined with random numbers to generate a set of correlated normal random numbers. This technique is used for calculating Monte Carlo VaR.

Probability of the joint default of both A and B =

We know all the numbers except default correlation, and we can solve for it.

DefaultCorrelation*SQRT(0.03*(1 - 0.03)*0.08*(1 - 0.08)) + 0.03*0.08 = 0.014.

Solving, we get default correlation = 25%